# Bloch's conjecture for Enriques varieties

## TL;DR

This paper proves Bloch's conjecture for all known irreducible Enriques varieties of index greater than 2, using Chow motives of generalized Kummer varieties, extending understanding of zero-cycle Chow groups.

## Contribution

It establishes Bloch's conjecture for a broad class of Enriques varieties, linking their Chow groups to motives of generalized Kummer varieties.

## Key findings

- Bloch's conjecture holds for all known irreducible Enriques varieties of index > 2.
- The proof utilizes Chow motives of generalized Kummer varieties.
- Results support the triviality of zero-cycle Chow groups in these cases.

## Abstract

Enriques varieties have been defined as higher-dimensional generalizations of Enriques surfaces. Bloch's conjecture implies that Enriques varieties should have trivial Chow group of zero-cycles. We prove this is the case for all known examples of irreducible Enriques varieties of index larger than $2$. The proof is based on results concerning the Chow motive of generalized Kummer varieties.